Audio effects are systems designed to alter how an audio signal sounds. Audio effects can be either analog or digital, depending on which domain the audio is in. Unprocessed audio is referred to as dry, while processed audio is referred to as wet.
Historically, before the advent of widespread digital technology, analog was the only method by which to manipulate a signal. Since that time, as computers and software have become more capable and affordable and digital signal processing has become the method of choice.  However, some producers go to great lengths to incorporate analog effects in their music, as many people claim that it produces a "warmer" or more "authentic" sound than their digital counterparts. [citation] Regardless of whether an effect is analog or digital, most share a common set of controls and techniques which can be discussed and shared amongst all producers
Audio effects have different parameters and definitions, but a few are common to all effects:
- Dry signal - Unprocessed signal. This term could be referring to signal that hasn't yet reached an audio effect in an audio signal chain. It could also be used to refer to signal that has bypassed an audio effect in a signal chain.
- Wet signal - Processed signal (i.e. signal that has been run through an audio effect).
- Dry/Wet - The ratio of dry to wet signal in an audio signal chain.
- Analog - An analog effect is one that has been created using hardware.
- Digital - A digital effect is one that has been created using software.
Don't overdo it.
Audio effects shine when they are used to make an already good sound even better. Usually this requires making good choices about which effects to use, rather than using a ton of effects. It's so easy to throw more effects at a problem rather than to consider what the problem is in the first place. If you catch yourself doing overdoing it, don't be afraid to start over or to remove effects entirely. Sometimes it's helpful to make a copy of a track (or even a full song) and start with a different, more minimal approach.
It's easy to get caught up in the novelty of a new sound. When an audio effect is applied to one of your dry tracks, the results can be surprising and interesting. That said, it doesn't mean that it is necessarily the right fit for your song. When determining which effects are right for the various parts of your song, consider the following approaches.
Pick an inspirational song that includes a certain type of effect that would be interesting to emulate. Use this "reference" track to help guide decision making on how much of a certain effect to apply, and which parameters to use. Experiment with different settings until the sound is very similar to the reference track.
Though experimentation can lead to breakthroughs, it's usually a good idea to set an intention before applying audio effects. In other words, try to determine what you are looking to accomplish with an effect before using it. For example, the vocals in the mix may need to be brought to the front. Or maybe a certain synth sounds too flat and 1-dimensional. Intentional decision-making, used in combination with a good ear and lots of reference tracks, can help songs sound more polished and cohesive.
One of the most important things a producer can do is to take regular breaks. Our hearing simply isn't built for non-stop, nuanced listening. In fact, after a few hours it can even start misleading us. It's usually a good idea to make nuanced decisions about audio effects after taking some time away from a song.
Nearly all DAWs have some form of automation built in, which allows effect parameters to be changed over time. Modern electronic music uses automation extensively for a wide range of purposes, from subtle mixing techniques to unique creative effects.
Spot effects are effects which are applied to single notes or phrases within a track, rather than to a pattern or track as a whole. Try using different reverb styles on the snare within drum patterns: a short decay on the '2' and a long decay on the '4' for example. Another idea is to apply spot chorus to individual words within a vocal line, as a way of adding emphasis to the lyrics. The 'freeze' or audio bounce-down function of a typical sequencer allows you to get around any problems your computer might have in running lots of instances of a particular effect. 
Automation can also be controlled by an external hardware device and "recorded" in a DAW. Many producers report that using knobs and faders instead of drawing automation curves by hand can lead to more natural sounding results. A good technique is to use a knob on an external midi controller to change a parameter over time, then comb through the resulting automation and fix any imperfections by hand.